The increase of demands for wideband traffics such as multimedia promotes an optical fiber communication system towards a direction of single-channel transmission of over 100 Gbit/s. When a single-channel rate reaches over 40 Gbit/s, an intra-channel nonlinear effect will obvious act on transmitted signals, thereby affecting communication quality.
A physical mechanism of the intra-channel nonlinear effect originates from a nonlinear Kerr effect of interaction of an electromagnetic wave and an optical fiber medium. In a high-speed long-haul optical fiber transmission system, as an optical pulse signal has a very short symbol period (<100 ps) and at the same time has relatively high transmission power (>0 dBm), a dispersion length LD and a nonlinear length LNL are far less than the transmission distance of the system, and hence the optical pulse signal is jointly affected by the intra-channel nonlinear effect and optical fiber dispersion effect, thereby resulting in production of energy exchange between neighboring pulses and obvious signal waveform distortion. In such a case, even if residual dispersion in the link is compensated at a receiving end, nonlinear distortion will still be produced in the pulse signal, and the transmission system will still be subjected to obvious nonlinear damages.
Taking a joint action of intra-channel nonlinearity and dispersion in an optical fiber into account, a time domain pulse sequence is mainly subjected to waveform distortion resulted from intra-channel crossing phase modulation (IXPM) and an intra-channel four-wave mixing (IFWM) effect. Such distortion may be qualitatively described as: timing jitter, pulse amplitude fluctuation and generation of a shadow pulse. For example, the timing jitter and pulse amplitude fluctuation originate from asymmetrical chirps resulted from the IXPM effect, and the shadow pulse originates from pulse energy exchange resulted from the IFWM effect. How to quantitatively calculate an effect of the above pulse distortion phenomenon on the long-haul optical fiber system and how to evaluate transmission system performance are importance subjects in the study of an optical fiber communication system.
Based on slowly varying envelope approximation and assumptions of constant polarization state, a transmission equation of pulse evolution in an optical fiber may be described by a nonlinear Schrödinger equation (described by a Manakov equation in random polarization). However, as the nonlinear Schrödinger equation has no analytical solution when a joint action of the nonlinearity and dispersion effects is taken into account, the quantitative study and related theoretical models for the intra-channel nonlinearity are developed and established for an approximate solution of the nonlinear Schrödinger equation. Currently, methods for solving the nonlinear Schrödinger equation are divided into a numerical value solution and an approximate solution. For example, the numerical value solution includes mainly a distributed Fourier algorithm and a time domain finite differential method, and the approximate solution includes mainly an inverse scattering method and a Volterra extension method.
As the wide application of the digital signal processing (DSP) technology in long-haul optical fiber communication systems, performing estimation or compensation on nonlinear distortion of the system in a digital domain becomes an effective method for resisting optical fiber link nonlinearity. As a standard numerical value solution of the nonlinear Schrödinger equation, the distributed Fourier algorithm may be taken as a candidate method for estimating and eliminating nonlinear distortion.
Kaln et al. reviewed nonlinear compensation performance of which a calculation step is equal to a length of an optical fiber span. F. Yaman et al. applied this method to a polarization multiplexing system, in which when the step is less than ⅓ of the optical fiber span, the compensation performance reaches the best. A defect of the distributed Fourier numerical value solution is that the complexity is too high, and even if the step is equal to the length of the optical fiber span, the number of times of calculation of this method poses a challenge to the current DSP technology.
As an approximation analytical method is hopeful to obviously reduce calculation complexity of nonlinear analysis, it draws wide attention of the academe and develops rapidly in these years. Solving the nonlinear Schrödinger equation by using the inverse scattering method may be applicable to educing a soliton solution of a nonlinear transmission system, thereby being applicable to analysis of a soliton communication system. As another method for solving the Schrödinger equation, the Volterra series expansion method enables an analytic framework of a conventional communication system to be lent to an optical fiber communication system, and is relatively universal to different pulse shapes and link types. Paolo Serena obtained a routine perturbation (RP) method based on the Volterra expansion method, and granted relatively definite physical meanings to orders of perturbation, thereby making the method for solving the Schrödinger equation by using perturbation developed rapidly, and multiple theoretical frames being derived from to be applied to quantitative nonlinear distortion in a time domain or a frequency domain.
However, it was found by the inventors in the implementation of the present disclosure that a defect of the prior art exists in that weighting coefficients occupy an important position in nonlinear distortion estimation, but no study is conducted currently on how to obtain a high-precision weighting coefficient, and high-precision estimation cannot be performed on nonlinear distortion in case of loss.
Documents advantageous to the understanding of the present disclosure and conventional technologies are listed below, and are incorporated herein by reference, as they are fully described in this text.    Non-patent document 1: A. Mecozzi et. al., IEEE PTL Vol. 12, No. 4, pp. 392-394, 2000;    Non-patent document 2: G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. New York: Academic, 1995;    Non-patent document 3: K. V. Peddanarappagari et. al., IEEE JLT Vol. 15, pp. 2232-2241, 1997;    Non-patent document 4: IEEE JLT Vol. 16, pp. 2046-2055, 1998;    Non-patent document 5: E. Ip and J. Kahn, IEEE JLT Vol. 26, No. 20, pp. 3416-3425, 2008;    Non-patent document 6: F. Yaman et. al., IEEE Photonics Journal Vol. 1, No. 2, pp. 144-152, 2009;    Non-patent document 7: A. Vannucci et. al., IEEE JLT Vol. 20, No. 7, pp. 1102-1111, 2002    Non-patent document 8: S. Kumar et. al., Optics Express, Vol. 20, No. 25, pp. 27740-27754, 2012    Non-patent document 9: E. Ciaramella et. al., IEEE PTL Vol. 17, No. 1, pp. 91-93, 2005    Non-patent document 10: A. Carena et. al., IEEE JLT Vol. 30, No. 10, pp. 1524-1539, 2012    Non-patent document 11: X. Chen et. al., Optics Express, Vol. 18, No. 18, pp. 19039-19054, 2010    Non-patent document 12: X. Wei, Optics Letters, Vol. 31, No. 17, pp. 2544-2546, 2006.
It should be noted that the above description of the background is merely provided for clear and complete explanation of the present disclosure and for easy understanding by those skilled in the art. And it should not be understood that the above technical solution is known to those skilled in the art as it is described in the background of the present disclosure.